Geodesic
On Projection Bodies of Order One
Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 349-360

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DOI

The projection body of order one ${{\Pi }_{1}}K$ of a convex body $K$ in ${{\mathbb{R}}^{n}}$ is the body whose support function is, up to a constant, the average mean width of the orthogonal projections of $K$ onto hyperplanes through the origin.The paper contains an inequality for the support function of ${{\Pi }_{1}}K$ , which implies in particular that such a function is strictly convex, unless $K$ has dimension one or two. Furthermore, an existence problem related to the reconstruction of a convex body is discussed to highlight the different behavior of the area measures of order one and of order $n\,-\,1$ .
DOI : 10.4153/CMB-2009-038-6
Mots-clés : 52A40 
Campi, Stefano; Gronchi, Paolo. On Projection Bodies of Order One. Canadian mathematical bulletin, Tome 52 (2009) no. 3, pp. 349-360. doi: 10.4153/CMB-2009-038-6
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     title = {On {Projection} {Bodies} of {Order} {One}},
     journal = {Canadian mathematical bulletin},
     pages = {349--360},
     year = {2009},
     volume = {52},
     number = {3},
     doi = {10.4153/CMB-2009-038-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2009-038-6/}
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